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We propose a systematic procedure for the construction of exactly solvable kN-body systems which are natural generalisations of Calogero models. As examples, we present two new 3N-body models and determine explicit expressions for their eigenvalues and eigenfunctions. [ABSTRACT FROM AUTHOR]

We study the ground-state properties of an atomic-molecular Bose–Einstein condensate model through an exact Bethe Ansatz solution. For a certain range of parameter choices, we prove that the ground-state Bethe roots lie on the positive real-axis. We then use a continuum limit approach to obtain a singular integral equation characterising the distribution of these Bethe roots. Solving this equation leads to an analytic expression for the ground-state energy. The form of the expression is consistent with the existence of a line of quantum phase transitions, which has been identified in earlier studies. This line demarcates a molecular phase from a mixed phase. Certain correlation functions, which characterise these phases, are then obtained through the Hellmann–Feynman theorem. [ABSTRACT FROM AUTHOR]

We study the exact Bethe ansatz solution of the Hamiltonian in a form whereby quantum numbers of states refer to hole-pairs, rather than particle-pairs used in previous studies. We find an asymmetry between these approaches. For an attractive system states in the strong pairing regime take the form of a partial condensate involving two distinct hole-pair creation operators. An analogous feature is not observed in the particle-pair picture of an attractive system. [ABSTRACT FROM AUTHOR]

Exactly solvable models provide a unique method, via qualitative changes in the distribution of the ground-state roots of the Bethe ansatz equations, to identify quantum phase transitions. Here we expand on this approach, in a quantitative manner, for two models of Bose–Einstein condensates. The first model deals with the interconversion of bosonic atoms and molecules. The second is the two-site Bose–Hubbard model, widely used to describe tunneling phenomena in Bose–Einstein condensates. For these systems we calculate the ground-state root density. This facilitates the determination of analytic forms for the ground-state energy, and associated correlation functions through the Hellmann–Feynman theorem. These calculations provide a clear identification of the quantum phase transition in each model. For the first model we obtain an expression for the molecular fraction expectation value. For the two-site Bose–Hubbard model we find that there is a simple characterization of condensate fragmentation. [ABSTRACT FROM AUTHOR]

We introduce a new family of quasi-exactly solvable (QES) generalized isotonic oscillators which are based on the Hermite exceptional orthogonal polynomials. We obtain exact closed-form expressions for the energies and wavefunctions as well as the allowed potential parameters for the first two members of the family using the Bethe ansatz method. Numerical calculations of the energies reveal that member potentials have multiple QES eigenstates and the number of states for higher members are parameter dependent. [ABSTRACT FROM AUTHOR]

An exactly solved bosonic tunneling model is studied along a line of the coupling parameter space, which includes a quantum phase boundary line. The entire energy spectrum is computed analytically, and found to exhibit multiple energy-level crossings in a region of the coupling parameter space. Several key properties of the model are discussed, which exhibit a clear dependence on whether the particle number is even or odd. Principal among these is a number-parity effect in the quantum dynamics. [ABSTRACT FROM AUTHOR]

We consider a generalization of the p + ip pairing Hamiltonian, with external interaction terms of a particular form. These terms allow for the exchange of particles between the system and its environment. As a result the symmetry associated with conservation of particle number, present in the p + ip Hamiltonian, is broken. Nonetheless the generalized model is integrable. We establish integrability using the boundary quantum inverse scattering method, with one of the reflection matrices chosen to be non-diagonal. We also derive the corresponding Bethe ansatz equations, the roots of which parametrize the exact solution for the energy spectrum. [ABSTRACT FROM AUTHOR]

For any translation-invariant quantum lattice system with a symmetry group G, we propose a practical and universal construction of order parameters which identify quantum phase transitions with symmetry-breaking order. They are defined in terms of the fidelity between a ground state and its symmetry-transformed counterpart, and are computed through tensor network representations of the ground-state wave function. To illustrate our scheme, we consider three quantum systems on an infinite lattice in one spatial dimension, namely, the quantum Ising model in a transverse magnetic field, the quantum spin - ½XYX model in an external magnetic field, and the quantum spin-1 XXZ model with single-ion anisotropy. All these models have symmetry group Z2 and exhibit broken-symmetry phases. We also discuss the role of the order parameters in identifying factorized states. [ABSTRACT FROM AUTHOR]